The wave has clearly only one frequency $\omega$, but is it monochromatic? My doubt is that it's circularly polarised so the amplitud is changing during time, so the $E$ field is the composition of two periodic oscillations. I don't know if this implies it's not monochromatic, even when there's only one frequency involved, or if it's still monochromatic.

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"Monochromatic" is used to denote waves of a single frequency (or superpositions of a very narrow wave of frequencies, at most). Polarization is independent of this, so your light is indeed monochromatic.